Monday, 31 May 2010

In the last few months a milestone has been passed on this blog - or more correctly surpassed. The PCG wiki which I maintain, and every so slowly expand on, now regularly gets more traffic than Ascii Dreams - despite my active solicitation of links to articles on the blog. Of everything I've written, 'Death of the Level Designer' has continued to be the most read article I've done and attracts thousands of impressions each month despite its age. But because of that age, it has become a little outdated, and in need of a refresh - especially in the light of some of the recent developments in the field of procedural content generation.

Despite the title, I wrote 'Death of the Level Designer' as an optimistic look at what the fruits of procedural content generation could be - before Spore was released and as a way of looking at that game, but also beyond it. Unfortunately, Spore wasn't the revolutionary game that many people hoped it would be - but it did deliver in many ways a new, powerful procedural content model which no other game has since matched.

At the same time, I saw a need to try to better define what procedural content generation was: and the taxonomy I proposed was in part a reaction to what I termed little-p procedural generation such as procedural animation and procedural textures. I argued this procedural generation did not directly impact game play, while dominating the definition of procedural generation in places such as Wikipedia, to the detriment of procedural content generation of levels, plots and other game focused content. As is always the case when you position a definition in opposition to something, that definition loses a level of sophistication; and I've modified my view, and more importantly the editorial content of the PCG wiki, to more correctly reflect procedural content as a continuum of procedural generation techniques, from procedural graphics to maze generation algorithms, world building and beyond.

What I see as increased interest in procedural content generation - driven in part as a way of providing more varied content in triple A titles, but mostly by the independent development community as a way of cheaply generating enough content for their games to distinguish themselves in a crowded field - hasn't necessarily translated into more sophisticated ways of generating this content.

The same techniques of 2d height maps, tile-based maze generation and random loot drops have been used in multiple different formats (Spelunky, Torchlight, Borderlands), without expanding into true 3d or utilising procedural narrative or plot generation in ways promised by games like Facade or Balance of Power. That's not to say there hasn't been a number of exciting innovations: chief of which is the AI Director from Left4Dead 1 & 2, the free form play of Far Cry 2 and roguelike-like revisionism of Spelunky, and the contract bridge style bidding system in Frozen Synapse, but no one has released a grand procedural game in the vein of Spore (except Eskil Steenberg's Love*) or pushed the boundaries that I expected to be broken.

There have been a huge number of games which have incorporated procedural generation in interesting ways without being truly innovative in its use: the TIG Source procedural generation competition was highlight for me, the 7 day rogue-like (7DRL) competition has grown every year, Eufloria, Canabalt and other indie titles have capitalized on procedural techniques and the excitement about up-and-coming games like Subversion and Infinity: the Quest for Earth is palpable. But procedural content generation is being trumped by user content generation in making the transition from 2d to 3d (Minecraft, 3D Dot Heroes) and building new narrative techniques (Spore: Space Adventures, Sleep is Death), in ways which appear limited by its reliance on repetition and randomness.

And procedural content driven games leave themselves open to the same rehashed criticism that is brought up every time they are mentioned in the gaming forums: the content created is repetitive, predictable and easily exploited, and clearly inferior to designs created by hand, an experience directly contrary to what I've found in the rogue-like genre.

So this article series is an attempt to update and expand the discussion around procedural content generation, take a look at more sophisticated ways of classifying procedural content, see what algorithms and techniques are potential low hanging fruit to try to guess where procedural content generation in games is going, but more importantly, hazard a better guess at where these games can potentially end up. In part two, I'll start by looking at new taxonomies.

One of the other things we tried was a secondary weapon that instantly teleported the Engineer to his teleport exit. So Engineers could leave their sentrygun for a bit to skirmish or collect metal, and be able to immediately teleport back to the sentrygun if something bad happened. It did work at achieving those goals, but we didn’t like the side effects. Teleporters stopped being much of a team focused tool, with Engineers placing them in places that made sense for their personal use, and not necessarily for the team. We also felt it was too easy for Engineers, almost eliminating the risk inside the decision of whether they should leave their nest to grab some resources. Both of these were solvable issues, but while testing this we found another idea that played much better, attacked the same problem of Engineers being rewarded for moving out from their nest occasionally, and had lots of other interesting applications.

Saturday, 22 May 2010

I wrote No Aliens Allowed as a plea to developers to make games with more intelligent science fiction instead of lazy genre tropes. No aliens and no mutants was a short hand way of expressing this; and excluding the far future and post apocalyptic settings was intended to cast aside the most common places science gets confused with fantasy. I also listed the games which I considered closest to qualifying and asked you for alternatives that I may have missed.

Thanks to those at reddit and Rock Paper Shotgun who commented and made suggestions, as well as those who responded here. There were some useful suggestions, Red Faction: Guerilla being the most glaring omission, Ghost Recon and various near future military shooters falling near the mark, and various games offered up by those people who hadn't read or understood the point I was making (Mass Effect 2, Borderlands etc).

Not one person suggested Portal.

I will admit, the direction I pushing towards was militarised games, and in Portal you don't have a gun. But in terms of near future, intelligent science fiction, Portal is a master class in Philip K Dick mind bending fun. It should have been foremost in everyone's mind, since Valve have cleverly given the game away for free for now, and yet not one person made the association when I asked for science fiction games without aliens.

What is it about Portal that isn't science fiction? The protagonist is in a scientific facility, using physics to solve puzzles, guided by an antagonist modelled on one of the most famous science fiction characters from one of the best known science fiction movies. This game is the archetype of what literary science fiction since the Golden Age of sci fi has been all about.

There is a key qualifier there: literary science fiction. The problem with Portal is that what people think of science fiction isn't literature - it's other media. And sadly, if your favourite fictional work is not written down, and has or rhymes with the word 'star' somewhere in it's title, you've been left behind by science fiction writing somewhere in the 60s.

Let me backpeddle immediately, and apologise for this unfairly broad brushstroke. You're at least one quarter a science fiction fan and probably more. I'll agree straight away that you are a fan of the conventions of the genre. No Aliens Allowed was a direct appeal to genre, and the strength of the science fiction genre: the romance of aliens, space ships, faster than light travel, psychic powers and futuristic technology is what gets many people into science fiction in the first place. Games like Mass Effect 2 appear to be science fiction games because they use the tropes of the genre to resonate with your love of which ever star film or television series appeals to you most. Genre appeals to the gut, and the love I have for Shattered Horizons and Dystopia is almost entirely genre driven - these games play my Cyberpunk strings the same way that that Wing Commander gets to your Space Opera fiddle.

It is the lack of genre conventions that made us all forget Portal was science fiction.

But science fiction isn't just about conventions of the genre, and genre is often the most lazy way to appeal to an audience. We can equally subvert the genre and remain science fiction, and I'll argue that Neal Stephenson's Baroque Cycle is as much a science fiction series as Iain M Banks' Culture novels, despite the conventions of historical drama and costume romance he adopts. That's because science fiction as much about thematic concerns as it is about genre. By removing the story from the immediate setting of the present day, it is often easier to explore the controversial and the taboo, as well as different ways of looking at the present and simply interesting alternatives. That is why Star Trek and Battlestar Galatica are better science fiction than Star Wars and Avatar, because they choose to deal with themes (race for the original Star Trek series, the American political situation for the re-imagined Battlestar Galatica) with a depth that George Lucas and James Cameron chose not to do so with their respective franchises.

The strand of science fiction that links it to fantasy on the bookshelves is world building - one pioneered by JRR Tolkien and Olaf Stapledon. Worldbuilding isn't a requirement of science fiction as it is for fantasy, but most science fiction authors must engage in it to project any further than a few minutes into the future. Unfortunately, worldbuilding often leads the resulting narrative to degenerate into the road trip movie of interesting people placed in a succession of unexpected situations; and the road to Mordor is closer to Sean William Scott getting interrectal assistance for a semen sample than you think.

But what uniquely appeals to me with science fiction - and hopefully to you if you're tolerated what I've said so far - is the science. Science fiction must be about science, above all else.

Having the characters exposed to vacuum in a movie doesn't make it a science fiction movie. The vacuum of space is now a science fiction trope, like space suits are a trope, or the hero being long haired and muscular in romance novels and wrestling are a trope. Having the character expose himself to vacuum as a calculated risk, where the alternatives are far worse, and the risks are depicted in a manner consistent with reality (and more importantly counter intuitive to what you think you know). That is science fiction.

(And by induction, McGyver is as much a science fiction television series as Babylon Five.)

It's easy to identify if something is not science fiction, because it has features something that directly contradicts what was known about science at the time. We are now certain that psychic powers don't exist in any measurable form - there's a million dollars waiting for you if you can prove otherwise - and so any fiction since about the early nineties that features psychic powers is not science fiction.

Science fiction isn't about aliens, or space ships, or star systems: it is about the scientific method. What is the simplist explanation of the observable phenomena which doesn't directly contradict what I know? How can I test this explanation, and if I observe a contradiction, can I modify or revise my theory to account for it? Science fiction allows you to exist in a universe where dragons fly and breath fire, but demands you explain how this is possible, and what the evolutionary advantage of this behaviour is - even if it is the necessity of intercepting and burning wormlike invaders from another world crossing through space.

Science fiction is gaming.

That may appear to be a bizarre conclusion to make. But bear with me.

Imagine you could travel backwards through time and change your decisions. What would be the consequences? How would it impact what you do? Time travel is rich territory for science fiction, for exactly this wealth of possibilities.

But you don't have to imagine. You can play Braid.

Games give you a predetermined set of rules and let you discover the consequences to those rules. You are the scientist testing the observable phenomena, coming to conclusions, deriving underlying rules from test results. There is a finite ruleset for the behaviour you're observing, because the underlying computer program is finite in size. So even if apples fall upwards when you least expect it (and other conventions of masocore gaming), you can still learn this from repeated experiment.

The difference between art and games is that gaming is scientific. Games are better than art.

And that is why I love science fiction above other types of writing, and why I make games instead of any other art.

Saturday, 15 May 2010

Dystopia and now the equally beautiful Shattered Horizon are two of my favourite multi player shooters. If you own Half Life 2: Episode 2 or later you owe it to yourself to download the Dystopia mod and invest a couple of hours getting a feel for the game; similarly I won't spend the time trying to convince you to buy the newly revamped Shattered Horizon when the Poisoned Sponge aka Phill Cameron has already invested the time writing an article on the update to do so.

There is something in the grognardian science fiction nerd in me that instantly finds near future warfare innately appealing. Shattered Horizon takes this to a whole new level: the ballet of physics and ballistics while staring at the face of the world immerses me in the future I dreamed of as a child. Whereas uninventive epics like Oblivion sit unplayed in the desk drawer next to me.

You may be a little surprised at my love of science fiction over fantasy, especially given the genre I currently develop in is Tolkien high fantasy. Unfortunately, Tolkien is one of the few fantasy writer I still find appealing. I passed through the phase of Weis and Hickman as a young teenager, and the closest I come to reading fantasy these days is the space opera antics of Peter F. Hamilton and Iain M Banks and the post modernist flights of fancy of Thomas Pynchon and Haruki Murakami.

(I steer pretty much clear of the military science fiction genre - which Dystopia and Shattered Horizons cleave to most closely - except noting that Joe Haldeman has said most everything that needed to be said on the subject, and with the sad voice of first hand experience.)

But where Dystopia and Shattered Horizons provide my multi player fix for near future science fiction settings, there has been this weird gulf for similar single player games: an inexplicable absence of narrative driven near future gaming experiences.

Let's be clear straight away: I'm specifically referring to near future, non-apocalyptic settings for single player gaming. There are plenty of apocalyptic settings: Stalker being the most fully realised science fiction, Half Life 2 the best selling, Fallout the archetype. And far future gaming is well served: Halo, Gears of War and others provide aliens and lasers in abundance.

But neither apocalypse or aliens provides me with the hacking, cybernetics and futuristic but recognisable military hardware buzz that these two multi player experiences give.

Only the inferior Haze and Sin: Emergence have featured a similar setting of late - and before that you have to search back to Deus Ex and Deus Ex 2 for the same ideas. Far Cry and Crysis make the mistake of throwing mutants/aliens at you, Metal Gear Solid comes closest but is bat shit insane (I've yet to play Metal Gear Solid 4 and PSP versions, but I hear the insanity still holds), Bioshock has the right ideas but exists in this retrofuturistic spellcasting culdesac, anything with zombies or mutants is just aliens dressed up in different clothing, which are usually elves, ghosts and dragons dressed up in different clothing. Am I missing anything?

The reason I'm asking is that telling a single player story about the near future demands a certain level of rigour in game design and narrative which a far future or apocalyptic story does not. You are held to higher standards, because the story you're telling is so close to the real world that you risk future events invalidating it, you can't invent as much handwavium to make combat play fun when the weapons are close to real world standards, you certainly can't insert the level of variety of enemies when you're restricted to the dull human chromosome.

But you can - and Shattered Horizons and Dystopia are evidence of it. But so is Call of Duty 4: Modern Warfare and sequel, and Armed Assault 2, only they've chosen to place their fiction in the present day (or weirdly Tom Clancy-fied versions of it), not twenty years down the track. But even with guns blazing, Dystopia and Shattered Horizon are not just militarised scenarios, they are stories about where we are going.

There is some hope forthcoming: a possible remake of Syndicate, and Introversion's Subversion promise to explore some of this territory. And the Deus Ex sequel, of course. But these are the few exceptions which prove the rule. (And the fact they have retrostylized the X-Com remake says so much more about the difficulties of doing so).

The best explanation to me is the one science fiction writer Charles Stross gives: he has had to rewrite so much of his near future stories as he works on them, because the present keeps catching up with the future he is trying to tell. For a science fiction writer, this is an inconvenience; for a triple A game, with a lead time of three, four, five years or more, this is a disaster. If you predicate your story on the Chinese invasion of Japan, and by the time the game is released China no longer exists as a political entity, you have an expensive fiasco on your hands - whereas the Narn Confederacy invading the Klingon Archipelago has less risk of wiping out your development budget.

Despite the insanity, it is Hideo Kojima who gets the future the best - which is why Metal Gear Solid 4 was telling the story of private military contractors the same time that Blackwater was being prosecuted in the Iraqi court of public opinion. It amazes me that no one pointed out reviewing the game the prognosticative powers necessary to achieve this feat. And no other great designer, sans Warren Spector, appears to have the confidence to do so.

Which is a shame because while the 20th century was about what we could be as people, the 21st century will be about what a person is (vanilla, polygendered, cybernetic, simulated). I want to explore those stories through the avenue of games. And I don't yet see the games there to do so.

Monday, 10 May 2010

Brought to you by the leading fashion houses Un-Nerf QQ and W+M1, the handbag replaces the secondary weapon (shotgun or flaregun) in a style to complement your primary weapon and make your Pyro the close combat champion (s)he once was.+25% Flamethrower damage+50 health with Backburner equippedIncrease the afterburn of your primary weapon to 10 seconds

Nearby burning enemies heal the Pyro as per the Medigun, up to 150% of his health.

[Edit: Amended since Valve mostly unnerfed the changes shortly after this was written].

Saturday, 8 May 2010

I have this bitter, metallic taste in my mouth, like I've just bitten down on my tongue after being slapped in the face... or drinking meths.

I'm angry. They've nerfed the Pyro and now expect me to be happy with this buff?

Let me back up a bit.

For those of you not aware, there has been some light and fury about the recent changes to the Pyro class in Team Fortress 2. Valve has chosen to decrease the direct damage and after burn effects (damage over time) effects of their primary weapon - the Flamethrower - in return for improving the effects and frequency of use of its alternate fire - which allows you to push enemy players and reflect projectiles using a puff of air (Some irrate players now want the class to be called the Aero). This was released in a patch to the game about a week ago, without comment as to why, as part of a number of changes in this constantly evolving game.

Team Fortress 2 is perhaps unique in commercial games - outside of the MMORPG genre - in that it has received constant tweaks since release in game balance. This isn't just a matter of releasing new content (multiplayer maps), but significant changes to the overall balance of classes - and with the class updates - significant changes to the way some classes play. It is a bold experiment, permitted by the digital distribution technology Steam, and a pioneering glimpse at a way some games can continue to be relevent years after release.

Team Fortress 2 is not the first game to receive a dedicated following - Starcraft, Super Street Fighter 2 Turbo, and Valve's own Counterstrike are the first three examples that spring to mind. What two of these games - Starcraft and Street Fighter - have in common is longevity has been maintained through the incredible balance between the moving parts in the system.

Unfortunately balance isn't something you can just design in: it is very much a matter of incredible luck as it is about deliberate design. If you consider all of the computer games ever made, there is only an extremely limited number which are still being played more than 15 years on from their inception (this holds less true now with change with the recent trend in retrogaming). And it is entirely possible that game designers may not even understand what it is that made their game successful. See this analysis on some of the micro issues in Starcraft 2 to get a feel for the level of accidental design detail that contributes towards game balance.

But there are some principles of game design that hold true when it comes to balance - worth reiterating here:

1. Always balance upwards

The most powerful character in a game is probably almost the most fun - especially when you are playing that character and your opponent isn't. As a result, you should use this as a yard stick for where you buff your other choices up to. But be careful not to overshoot when improving them, because:

2. It is much harder to scale down and take away than to scale up and add

Much like cooking, it is much harder to take away ingredients to a game than it is to add them. Particuarly once a game is released, human nature is ingrained against removing functionality and decreasing ability. Programmers have written code, art assets have been designed, people have played with the ability at a particular level. There is nothing like the cry of nerf to rally the forums. But if you are going to take away functionality, be sure to:

3. Change one variable rather than scaling across the board

If you think about balancing a game by playing it, you are really conducting a series of experiments and seeing the results. And science works best when you can vary one value and leave the other variables as fixed as possible. So if you have a character which does three things too well, leave two of them at the level that is overpowered, and reduce the third and then see if that leaves the character balanced against the other choices. Of course, this is easiest when you:

4. Keep your variables independent

The Mutalisk in Starcraft was incredibly hard to balance because it uses the same attack to attack both air and ground units. During testing and post-release patching, if it was too effective against air units, reducing the attack strength would make it ineffective against ground units. And vice versa. Creating two separate attacks would have allowed the game designers to better balance this unit - at the cost of increased art and animation assets required to do so.

5. Statistics and mathematical analysis is incredibly important

If you consider playing as a series of experiments, then the other tools of scientific analysis: statistics and mathematical modelling are obviously critical to get an understanding of how the game works. Unangband balances its monsters by modelling a simulation of 10 rounds of combat and seeing how much damage the monster inflicts. This model is as simple as taking the highest of (chance of attack * damage inflicted * 'typical player resistance * 10) of each attack the monster is capable of but works remarkably effectively. And I don't have to get this exactly right because Unangband, like many games:

6. Provide plenty of resets

A reset is a way of either player recovering from a situation by using up an exhaustable resource. Guilty Gear has an incredible cast of characters with bizarre attacks but also has a number of ways of recovering from the effects and traps of any of these attacks. The resets act as a negative feedback mechanism to dampen the risk of any positive feedback interactions between abilities getting out of control. I've written more about resets and traps in my series on designing a magic system.

7. Intuition and fun are the most important mechanism for balance

Balancing a game is like finding the most effective pay out on an almost infinitely long multi-armed slot machine. You have so many variables to consider that a complete mathematical analysis of most games is impossible. Luckily there is one computer capable of solving these kinds of problems, and that's the one between your ears. But experience is a requirement here. You need to play lots of other games - especially games with depth to them - to appreciate how to balance your own.

8. Ignore (almost) all player feedback when it comes to 'too powerful' abilities

There are an incredible number of people who are prepared to label an ability in a game as being too powerful or cheap, without understanding the ramifications of that ability at high level play. So as a rule you should ignore them. The exceptions are those players who are at the top of their game. You are then permitted to listen respectfully, and then ignore their feedback unless there is other evidence to back up their anecdotes.

9. Your players will figure out the numbers so make the maths available to them

One of the most useful things the phenomenon of crowd sourcing has produced are endless wikis for games of detailled statistics of in game play. If your game becomes popular, the players will figure out the numbers, so you should make them available. Surprisingly, this happens infrequently outside of the strategy game genre - where tables of numbers are a typical characteristic of in game documentation.

So how do the above principles help when it comes to discussing the Pyro changes that Valve have made?

The Pyro class was one of the earliest to receive a class update from Valve - only the Medic preceeded it. But balancing the Pyro was immediately problematic. Within a few weeks of the class update, the new primary weapon the Backburner got its first nerf. Previously it had provided +50 health (and glorious were the days on the servers when the Pyro update came out). Then Valve added back some of the damage drop off that they had removed with the Pyro update to the Pyro's flamethrower.

Since then, the other updates have added various ways of putting out the Pyro's afterburn effect: the Sniper's Jarate, the Pyro's airpuff, the Heavy's sandvich, the Spy's dead ringer (although the cloaked spy can be immediately set on fire again). These have been both thematic improvements and Valve providing a number of reset options to the afterburn effect.

Discussion on the Pyro prior to the most recent changes on the forums has revolved around 2 main areas of contention: the Pyro still being underpowered, and the criticism of the W+M1 still of play of so-called noobs - those people who play a Pyro by running forward with the flamethrowing and not otherwise thinking. Neither of these suggest serious balance issues, and the criticism of 'cheapness' can especially be ignored.

Valve themselves have acknowledged issues with the Pyro at 'high-level' play. But Valve's statements to this effect have been contradictory in the past and may not necessarily point to the heart of the problem - they initially stated that the Pyro was intended for close combat, but the flamethrower has always had weak close in damage - now doubly so.

So is there any balance problems for the Pyro that we can establish empirically without anecdotal evidence or hersay? Looking at the information made available by Valve and third parties, I can see at least one imbalance, and one paradox, worth discussing further.

Firstly the choice between the Flamethrower and Backburner is heavily skewed in favour of the flamethrower. In fact, no other class has such a split between primary weapons (It is worth stressing that all the statistics on the main page are from players who only have both choices available). And how to rebalance? Balance up, of course. This suggests the backburner may need to be improved against the flamethrower some how.

More interestingly, the choice between Shotgun and Flaregun is almost a perfect split. So Valve's buff to allow the Flaregun to do minicrits against opponents on fire has been received well, which we'll use here as a proxy for the two choices being balanced against each other.

Finally the melee weapon selection is biased heavily against the default axe, and towards the Axtinguisher. With the Homewrecker, there is the possibility of novelty or bragging rights factor that may influence the frequency it appears in the short term. Again, we should balance the default Fireaxe up if there is a balance problem - but we don't have the statistics to suggest that this is the case.

From checking the preferred weapons we can see that no other class favours one weapon choice any less for the primary and melee weapons - the Soldier's Equalizer is a straight upgrade to the Pickaxe and so there is no reason to ever not use it if it is available. So we have a clear imbalance between some of the choices that the Pyro has available. This does not necessarily mean that there is not a situational advantage to the weapons which are least selected, but the situation advantage must occur rarely. As always, the suggestion is to balance the unfavoured choices up so that they become more preferred. But this is not itself an indication of whether the Pyro is a balanced class, and so we do not have evidence yet that the class has been nerfed.

Looking at the class distribution choices, the Pyro falls towards the bottom of the range of those chosen. But interestingly, despite being relatively unpopular, the flamethrower damage percentage of total damage inflicted is the second highest behind the grenade launcher. And it has the second average longest range of any weapon (including the Sniper Rifle) except for the minigun. But we know that the flamethrower damage output is incredibly low. There is definitely a paradox here, and one caused by the aggregation of flamethrower damage, and afterburn damage in the same statistics.

And this is the main problem with the publically available statistics. There's not enough detail to have a viable discussion about the Pyro 'nerf'. In fact, the statistics Valve releases aggregate all the weapon statistics together, so it is not even possible to say which weapon choice does more damage (You can see this from the Sniper SMG - actually the Jarate - being the fourth highest source of damage, and the Fireaxe - actually the Axtinguisher - having such a high critical rate). It is not clear from the statistics page but this appears to be a limitation of the way TF2 collects stats.

Without Valve coming out and providing more detailled information about the decision making in making the Pyro changes, the outrage of the forums will continue to boil and players will continue to come up with suggested buffs and nerfs without a deeper understanding of the process that went into making these decisions. Mathematical modelling of the Pyro damage drop off isn't enough to explain the paradox of the flamethrower having the second highest percentage damage output.

So my request is not to buff the Pyro back - it's to improve the communication process and statistics collection. That way we can have a much more useful discussion about the changes to one of my favourite classes.

For the record though: I'd like to see the Pyro back to what they were on the release day of their class update... just for a week, or as a mod. But my biggest problem isn't a Pyro's damage output, it is their longevity. They need something to survive a few seconds longer: perhaps the Backburner should trade increased protection against bullets for increased knockback (allowing an onrushing Pyro to be pushed back by a Heavy's gun) and the Homewrecker should reduce knockback when wielded.

For those of you interested in a more indepth discussion of balance in games, I recommend David Sirlin's excellent four part guide on game balance, as well as his website in general.